Finite Group Databasebeta

← #16845811

Subgroups — #16845811

Order 3968.

306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758503C211yesmaximal, characteristic
2#14521013C211yesmaximal, characteristic
3#14520809C214yesmaximal, complemented
4C4×C22⋊C4×C31C211yesmaximal, characteristic
5C23×C4×C31C2211yescharacteristic
6C2×C22⋊C4×C31—21no—
7C2×C42×C31C2212yes—
8C2×C22⋊Dic31—21no—
9#11758503—21no—
10#11758503—21no—
11#11758503C412yescomplemented
12#11758503C2212yes—
13C2×C4⋊Dic31C411yescharacteristic, complemented
14C2×C4⋊Dic31C411yescharacteristic, complemented
15C2×C4×Dic31—21no—
16C2×#92474C2212yes—
17C31×#95—21no—
18C22⋊(C31⋊C8)—21no—
19C22⋊(C31⋊C8)—21no—
20C24×C31D411yescharacteristic
21C22×C4×C31—24no—
22C22×C4×C31—22no—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31C2311yescharacteristic
29C22×Dic31—21no—
30C22×Dic31—21no—
31C22⋊C4×C31—24no—
32C42×C31—24no—
33C22⋊Dic31—22no—
34C22⋊Dic31—22no—
35C4⋊Dic31—21no—
36C4⋊Dic31—21no—
37C4⋊Dic31C2×C412yes—
38C4⋊Dic31C2×C412yes—
39C4×Dic31—22no—
40C4×Dic31—22no—
41#92474—24no—
42C2×C31⋊C8—22no—
43C23×C31—22no—
44C23×C31—22no—
45C23×C31—41no—
46C23×C31C22⋊C411yescharacteristic
47C23×C31C22⋊C411yescharacteristic
48C23×C31C2×D411yescharacteristic
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31—22no—
54C2×C4×C31—24no—
55C2×C4×C31—42no—
56C2×C4×C31—42no—
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22×C411yescharacteristic
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31#4114yes—
62C2×Dic31—22no—
63C2×Dic31—22no—
64C2×Dic31—42no—
65C2×Dic31—42no—
66C31⋊C8—42no—
67#1826—311nomaximal, Sylow
68C22×C31—21no—
69C22×C31—21no—
70C22×C31—21no—
71C22×C31—21no—
72C22×C31—21no—
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—44no—
76C22×C31#10412yes—
77C22×C31C2×C22⋊C411yescharacteristic
78C22×C31#12312yes—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—44no—
82C4×C31#11712yes—
83C4×C31#12312yes—
84Dic31—42no—
85Dic31—42no—
86C2×#117—311no—
87#407—311no—
88C4×C22⋊C4D3111yescharacteristic
89#339—314no—
90C2×C31—22no—
91C2×C31—22no—
92C2×C31—41no—
93C2×C31#38111yescharacteristic
94C2×C31C2×#10411yescharacteristic
95C2×C31#42111yescharacteristic
96C23×C4C2×D3111yescharacteristic
97C2×M16—312no—
98#117—312no—
99#117—312no—
100#117—621no—
101#117—621no—
102C2×C4⋊C4—311no—
103C2×C4⋊C4—311no—
104C2×C22⋊C4—21no—
105C2×C22⋊C4—621no—
106C2×C42—621no—
107C2×C42C2×D3112yes—
108C22⋊C8—621no—
109C22⋊C8—621no—
110#95—21no—
111C31#182611yescharacteristic, complemented, Sylow
112C24C22⋊D3111yescharacteristic
113C22×C4—24no—
114C22×C4—22no—
115C22×C4—621no—
116C22×C4—621no—
117C22×C4C4×D3111yescharacteristic
118C22×C4C4×D3111yescharacteristic
119C22×C4D12411yescharacteristic
120C22×C4D12411yescharacteristic
121C22×C4C22⋊D3111yescharacteristic
122C22×C4C22×D3111yescharacteristic
123M16—624no—
124C2×C8—622no—
125C4⋊C4—312no—
126C4⋊C4—312no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C22⋊C4—24no—
130C22⋊C4—622no—
131C22⋊C4—622no—
132C42—24no—
133C42—622no—
134C42—622no—
135C23—22no—
136C23—22no—
137C23—41no—
138C23(C2×D31)⋊C411yescharacteristic
139C23(C2×D31)⋊C411yescharacteristic
140C23C2×C22⋊D3111yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—622no—
150C2×C4—622no—
151C2×C4—1242no—
152C2×C4—1242no—
153C2×C4(C2×D31)⋊C411yescharacteristic
154C2×C4(C2×D31)⋊C411yescharacteristic
155C2×C4C2×C4×D3111yescharacteristic
156C2×C4C2×D12411yescharacteristic
157C2×C4#9249714yes—
158C8—1242no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—44no—
167C22#1175839312yes—
168C22C2×(C2×D31)⋊C411yescharacteristic
169C22#1175851212yes—
170C4—21no—
171C4—21no—
172C4—44no—
173C4—1242no—
174C4—1242no—
175C4#1175845412yes—
176C4#1175846312yes—
177C2—22no—
178C2—22no—
179C2—41no—
180C2#1452091011yescharacteristic
181C2C2×#1175839311yescharacteristic
182C2#1452106711yescharacteristic
subgroupG/H
centerC2×C4C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC4×C22⋊C4×C31C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC4×C22⋊C4D31
hypocenterC31#1826
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14520809C2semidirect
11. #11758503C4semidirect
13. C2×C4⋊Dic31C4semidirect
14. C2×C4⋊Dic31C4semidirect
111. C31#1826semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117585032
#145210132
#145208092
C4×C22⋊C4×C312
#182631